Discount Calculator
How to Calculate a Discount
A discount is a reduction from the original (or list) price of an item, expressed as a percentage. Discount calculations come up constantly — in retail shopping, business negotiations, invoicing, and financial modeling. There are three common scenarios, each handled by a different formula.
Discount Formula
The three formulas you need for every discount situation:
1. Find the Sale Price (Percent Off)
Sale Price = Original Price × (1 − Discount% ÷ 100)
Or equivalently:
Savings = Original Price × Discount% ÷ 100
Sale Price = Original Price − Savings
Example: $120 item at 30% off:
2. Find the Original Price (Reverse Discount)
Original Price = Sale Price ÷ (1 − Discount% ÷ 100)
Example: Item is $84 after a 30% discount. What was the original price?
A common mistake is to add 30% directly to $84, which gives $109.20 — an incorrect answer. You must divide by the complement (0.70), not multiply by 1.30.
3. Find the Discount Percentage
Discount % = ((Original − Sale) ÷ Original) × 100
Example: Item was $150, now $105. What percent off?
Variable Definitions
| Variable | Meaning |
|---|---|
| Original Price (P) | The full, pre-discount price (also called list price, MSRP, or regular price) |
| Discount % (d) | The percentage reduction, e.g. 20 for 20% off |
| Sale Price (S) | The price after the discount is applied |
| Savings | The dollar amount saved: P − S |
Double Discounts (Stacking)
Retailers sometimes advertise "extra 10% off already reduced prices" or stack multiple promotional codes. These discounts are applied sequentially, not additively. A 20% discount followed by a 10% discount is not 30% off — it is 28% off.
The formula for two stacked discounts:
Effective Discount = 1 − (1 − d1/100) × (1 − d2/100)
Examples of common stacked discount combinations:
| Discount 1 | Discount 2 | Effective Discount | On $100 |
|---|---|---|---|
| 10% | 10% | 19.0% | $81.00 |
| 20% | 10% | 28.0% | $72.00 |
| 25% | 15% | 36.25% | $63.75 |
| 30% | 20% | 44.0% | $56.00 |
| 50% | 50% | 75.0% | $25.00 |
Notice that 50% + 50% stacked is not 100% off — it is 75% off. The second 50% applies to the already-reduced price, not the original. This is why retailers can advertise "additional 50% off sale prices" without giving items away.
Three or More Stacked Discounts
The pattern extends to any number of discounts. Multiply the complements together and subtract from 1:
Effective = 1 − (1−d1/100) × (1−d2/100) × (1−d3/100) × ...
Example: A retailer offers 30% off a $200 item, then an additional 20% off at checkout, plus a 5% loyalty discount:
Percentage Increase vs. Decrease Are Not Symmetric
A 50% price increase followed by a 50% price decrease does not return to the original price. $100 × 1.50 = $150, then $150 × 0.50 = $75. You end up 25% below the start. This asymmetry is why "we raised prices 20% but then lowered them 20%" is a pay cut in disguise. Always calculate in absolute dollars when precision matters.
Frequently Asked Questions
How do I calculate a percentage discount?
Multiply the original price by the discount percentage, then subtract: Sale Price = Original × (1 - Discount%/100). Example: $80 item at 25% off = $80 × 0.75 = $60. The savings are $80 - $60 = $20. You can also think of it as: find the discount amount ($80 × 25% = $20), then subtract from the original ($80 - $20 = $60).
How do I find the original price when I only know the sale price and discount?
Divide the sale price by (1 - discount%/100). If an item is $60 after a 25% discount: Original = $60 ÷ (1 - 0.25) = $60 ÷ 0.75 = $80. This works because the sale price is 75% (100% - 25%) of the original, so dividing by 0.75 reverses the discount. Never make the mistake of adding the discount percentage directly to the sale price — that gives the wrong answer.
What is a double discount and how do I calculate it?
A double discount (or stacked discount) applies two percentage discounts sequentially, not additively. A 20% discount followed by a 10% discount is NOT 30% off. Example: $100 item, 20% off = $80, then 10% off $80 = $72. Total savings = $28, not $30. The combined discount formula is: 1 - (1 - d1/100) × (1 - d2/100). For 20% + 10%: 1 - 0.80 × 0.90 = 1 - 0.72 = 28% effective discount.
How do I calculate the discount percentage when I know both prices?
Discount % = ((Original Price - Sale Price) ÷ Original Price) × 100. Example: original $120, sale price $90. Savings = $30. Discount % = ($30 ÷ $120) × 100 = 25%. This is the "Section 3" calculation in the tool above. Make sure to divide by the original price, not the sale price — a common error that overstates the discount.
Is a 50% discount the same as buy one get one free (BOGO)?
Yes — mathematically they are equivalent when applied to identical items. If a $40 shirt is BOGO free, you pay $40 for two shirts, which is $20 each — a 50% effective discount per unit. However, BOGO requires you to buy two items. If you only want one, a 50% discount is better. Retailers use BOGO specifically because it increases total units sold while achieving the same per-unit price reduction.
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